Ask Dr. SETI ®

P_sens (in dBm) = -174 dBm + 10 log B (in Hz) + Total Receive System Noise Figure (dB)

The above -174 dBm is 10 log K (Boltzmans Constant) less 10 Log (T), all converted to dBm

T being the temperature of the antenna in Kelvin
B is the bandwidth of the receiver

Roy (via the ARGUS list)

The Doctor Responds:
That equation is entirely correct, Roy, and the 290 Kelvin limit is true for terrrestrial communications. It does not hold for radio astronomy! It would only be true if your antenna were pointing at the Earth (which is a 290 Kelvin thermal black body). That figure is used for terrestrial communications because antennas pointed on the horizon 'see' Earth noise. With radio telescopes, our antennas are pointed generally 'up' at the sky, and the sky is RF-cold. So, your antenna sees less noise to limit system sensitivity.

The actual sky temperature varies, of course, with where you're pointing, with the minimum being 2.7 Kelvin (the cosmic background radiation), and the hot spots in the sky emitting some tens of Kelvin at microwave frequencies. The actual thermal temperature seen by your antenna will be higher, because sidelobes and over-illumination spillover mean that some Earth noise is in the pattern, and this adds to total noise. I figure a 50 Kelvin antenna temperature for my system when it's in birdbath mode, slightly more when it's pointed lower.